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There are no specific regulations regarding the interference effects that an adjacent building can place on the wind load distribution of a dome roof structure. Furthermore, the influence between an adjacent rectangular-section building and the dome roof structure on the wind-induced interference is not well understood yet. Thus, in this paper, computational fluid dynamics (CFD) is used to simulate the mean wind pressure of the dome roof structure after interference by a rectangular-section building facing the dome. The accuracy of numerical results is verified through a wind tunnel test. The effects of different building heights or widths as well as distances between the interference building and the dome on the interference are analyzed. Different wind directions in intervals of 15∘ are examined in the analysis to identify the worst wind direction. The results reveal that the passage effect caused by the interference is the main reason for the increase of suction on the roof, and the height ratio has the greatest influence on the passage effect. The region of the roof nearest to the interference building experiences the greatest suction considering all wind directions, and the side regions of the roof are relatively safe in most cases. The results of this paper can provide a reference for engineers tasked with wind-resistant design of long-span dome structures. [ABSTRACT FROM AUTHOR]

Ductility and energy dissipation capacity of the beam column joints are the two prominent characteristics which govern the stability of the entire structure constructed in the seismic prone areas. In this paper, the effect of potassium-activated geopolymer concrete in the exterior beam column joint application is investigated under low frequency cyclic loading. Numerical analysis has been done by using the finite element software Abaqus and compared with the experimental work. From the load deformation relationship, parametric studies are carried out in the aspects of ductility, stiffness degradation, energy dissipation capacity, drift ratio and cracking pattern. The use of potassium-activated geopolymer technology in the exterior beam column joint application resulted in the improved ductility, energy dissipation capacity with superior ultimate load carrying capacity of 1.05% over conventional cement reinforced concrete beam column joints with special confining reinforcement confirmed by IS 13920 due to the enormous polymerization activated by high molecular potassium ions. There is an improved energy dissipation capacity of 2.78% of potassium-based geopolymer specimen resulting in lesser number of non-structural cracks and 11.26% more deformation under 11.96% enlarged drift ratio than the conventional reinforced concrete specimen. From the observed results, it is clearly noted that the implementation of potassium-activated green polymer technology in the beam column joints possessed enhanced ductility characteristics to protect the structure susceptible to seismic environment and resulted in innovative, economical and sustainable mode of seismic-resistant building construction. [ABSTRACT FROM AUTHOR]

With the rapid development of information technology, internet of things, cloud computing, digital networks and 5G have become an indispensable part of our life. Due to the development of these cutting-edge digital technologies, smart cities now have become a reality. During the development of smart cities, many different sensing devices of the cities would generate lots of data. To smoothly use the massive data, the paradigm of cloud computing will be deployed by smart cities, these data will be efficiently stored and processed by the cloud servers. However, the security of data in smart cities should be guaranteed, especially for the privacy protection of data. Aiming at securely managing cloud data in smart cities, this paper proposes a set of secure cloud data computing protocols for set operations based on the Paillier encryption system. For the rational numbers which are very common in smart cities, we design a coding technology to realize the secure homomorphic computation of them. We also verify the security and correctness of our protocols through rigorous mathematical proof, and demonstrate the efficiency of our solutions by performance analysis. [ABSTRACT FROM AUTHOR]

It is a significant and challenging task to detect both the coexistence of singular cycles, mainly homoclinic and heteroclinic cycles, and chaos induced by the coexistence in nonsmooth systems. By analyzing the dynamical behaviors on manifolds, this paper proposes some criteria to accurately locate the coexistence of homoclinic cycles and of heteroclinic cycles in a class of three-dimensional (3D) piecewise affine systems (PASs), respectively. It further establishes the existence conditions of chaos arising from such coexistence, and presents a mathematical proof by analyzing the constructed Poincaré map. Finally, the simulations for two numerical examples are provided to validate the established results. [ABSTRACT FROM AUTHOR]

Tip growth is a growth stage which occurs in fungal cells. During tip growth, the cell exhibits continuous extreme lengthwise growth while its shape remains qualitatively the same. A model for single celled fungal tip growth is given by the Ballistic Aging Thin viscous Sheet (BATS) model, which consists of a five-dimensional system of first-order differential equations. The solutions of the BATS model that correspond to fungal tip growth arise through a codimension-1 global bifurcation in a two-parameter family of solutions. In this paper we derive a toy model from the BATS model. The toy model is given by two-dimensional system of first-order differential equations which depend on a single parameter. The main achievement of this paper is a proof that the toy model exhibits an analogue of the codimension-1 global bifurcation in the BATS model. An important ingredient of the proof is a topological method which enables the identification of the bifurcation points. Finally, we discuss how the proof may be generalized to the BATS model. [ABSTRACT FROM AUTHOR]

The p -wave resonances induce an infinite number of negative eigenvalues accumulating at the origin for the system of three identical particles in two dimensions, provided that the energy operator is restricted on the subspace of wave functions which are antisymmetric with respect to the permutations. This quantum phenomenon is called the super Efimov effect and corresponds to the Efimov effect in three dimensions. It has been predicted in physics literature [10] and a mathematical proof has been given by Gridnev [5]. In this paper, we prove this effect for a wider class of pair interactions and improve the results obtained by [5]. We do not necessarily assume that the interactions are radially symmetric, have a definite signature and fall off exponentially at infinity. The essence of the proof is put in the asymptotic analysis of the singular behavior at low energy for resolvents of the Schrödinger operators with p -wave resonances at zero energy. [ABSTRACT FROM AUTHOR]

The free energy of a ternary system, such as a triblock copolymer, is a sum of two parts: an interface energy determined by the size of the interfaces separating the micro-domains of the three constituents, and a long range interaction energy that serves to prevent unlimited micro-domain growth. In two dimensions a parameter range is identified where the system admits stable stationary disk assemblies. Such an assembly consists of perturbed disks made from either type-I constituent or type-II constituent. All the type-I disks have approximately the same radius and all the type-II disks also have approximately the same radius. The locations of the disks are determined by minimization of a function. Depending on the parameters, the disks of the two types can be mixed in an organized way, or mixed in a random way. They can also be fully separated. The first scenario offers a mathematical proof of the existence of a morphological phase for triblock copolymers conjectured by polymer scientists. The last scenario shows that the ternary system is capable of producing two levels of structure. The primary structure is at the microscopic level where disks form near-perfect lattices. The secondary structure is at the macroscopic level forming two large regions, one filled with type-I disks and the other filled with type-II disks. A macroscopic, circular interface separates the two regions. [ABSTRACT FROM AUTHOR]

The query probability of a location which the user utilizes to request location-based service (LBS) can be used as background knowledge to infer the real location, and then the adversary may invade the privacy of this user. In order to cope with this type of attack, several algorithms had provided query probability anonymity for location privacy protection. However, these algorithms are all efficient just for snapshot query, and simply applying them in the continuous query may bring hazards. Especially that, continuous anonymous locations which provide query probability anonymity in continuous anonymity are incapable of being linked into anonymous trajectories, and then the adversary can identify the real trajectory as well as the real location of each query. In this paper, the query probability anonymity and anonymous locations linkable are considered simultaneously, then based on the Markov prediction, we provide an anonymous location prediction scheme. This scheme can cope with the shortage of the existing algorithms of query probability anonymity in continuous anonymity locations difficult to be linked, and provide query probability anonymity service for the whole process of continuous query, so this scheme can be used to resist the attack of both of statistical attack as well as the infer attack of the linkable. At last, in order to demonstrate the capability of privacy protection in continuous query and the efficiency of algorithm execution, this paper utilizes the security analysis and experimental evaluation to further confirm the performance, and then the process of mathematical proof as well as experimental results are shown. [ABSTRACT FROM AUTHOR]

This paper corrects some mistakes about three theorems, two figures and some expressions on "finite field" in a literature, and then it analyzes the digraphs and period properties of the logistic map on residue class rings Z (3 n) and Z (p n). Some theorems and conjectures are proved or given. To validate these properties, we make some numeral experiments and draw the relative figures and tables. So the theoretical analysis and numeral experiments show that there exists periods in the logistic map on Z (3 n) and on Z (p n) and it can be applied in the pseudo-random generators, cryptography, spread spectrum communications and so on. [ABSTRACT FROM AUTHOR]

Let X ⊂ ℙ n be a general Fano complete intersection of type (d 1 , ... , d k). If at least one d i is greater than 2 , we show that X contains rational curves of degree e ≤ n with balanced normal bundle. If all d i are 2 and n ≥ 2 k + 1 , we show that X contains rational curves of degree e ≤ n − 1 with balanced normal bundle. As an application, we prove a stronger version of the theorem of Tian [27], Chen and Zhu [4] that X is separably rationally connected by exhibiting very free rational curves in X of optimal degrees. [ABSTRACT FROM AUTHOR]

We prove that the optimal cluster problem for the sum/the max of the first Robin eigenvalue of the Laplacian, in the limit of a large number of convex cells, is asymptotically solved by (the Cheeger sets of) the honeycomb of regular hexagons. The same result is established for the Robin torsional rigidity. In the specific case of the max of the first Robin eigenvalue, we are able to remove the convexity assumption on the cells. [ABSTRACT FROM AUTHOR]

Within the field of quantum cryptography, two-way direct quantum secure communication is a relatively new proposal for sharing secret information that is not fully explored yet. We propose a general model for two-way deterministic quantum key distribution, and a special mapping from integers to a uniformly distributed quantum space is introduced for qubit pad preparation. A reduced model, more practical, is also proposed by relaxing the security assumption of the qubit pad preparation. The main work of this paper focuses on the security proofs of these two models. Under collective attacks, we fully analyze the security basis of the general model, and, in a relatively simple way, we provide an analytical security proof for the reduced model in a depolarization quantum channel. Our results show exactly the analytical upper-bound of the amount of useful key that a powerful eavesdropper could extract in both models, and the security of the reduced model is not reduced. One advantage of this work is that the special mapping guarantees the random distribution property of the qubit pad in a uniformly distributed quantum space, thus guaranteeing the security of the two models, and the other advantage is the simplicity of the analytical derivations of security proofs. [ABSTRACT FROM AUTHOR]

We give an affirmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G with an identity, we prove that the set of right Engel elements of G is contained in the Hirsch–Plotkin radical of G. Given an arbitrary word w , we also show that the class of all groups G in which the w -values are right n -Engel and w (G) is locally nilpotent is a variety. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a family of transverse invariants arising from the deformations of Khovanov homology. This family includes the invariants introduced by Plamenevskaya and by Lipshitz, Ng, and Sarkar. Then, we investigate the invariants arising from Bar-Natan's deformation. These invariants, called β -invariants, are essentially equivalent to Lipshitz, Ng, and Sarkar's invariants ψ ± . From the β -invariants, we extract two non-negative integers which are transverse invariants (the c -invariants). Finally, we give several conditions which imply the non-effectiveness of the c -invariants, and use them to prove several vanishing criteria for the Plamenevskaya invariant [ ψ ] , and the non-effectiveness of the vanishing of [ ψ ] , for all prime knots with less than 12 crossings. [ABSTRACT FROM AUTHOR]

We show that if a braid B can be parametrized in a certain way, then the previous work (B. Bode and M. R. Dennis, Constructing a polynomial whose nodal set is any prescribed knot or link, arXiv:1612.06328) can be extended to a construction of a polynomial f : ℝ 4 → ℝ 2 with the closure of B as the link of an isolated singularity of f , showing that the closure of B is real algebraic. In particular, we prove that closures of squares of strictly homogeneous braids and certain lemniscate links are real algebraic. We also show that the constructed polynomials satisfy the strong Milnor condition, providing an explicit fibration of the complement of the closure of B over S 1 . [ABSTRACT FROM AUTHOR]

We prove Alexander- and Markov-type theorems for virtual spatial trivalent graphs and virtual trivalent braids. We provide two versions for the Markov-type theorem: one uses an algebraic approach similar to the case of classical braids and the other one is based on L -moves. [ABSTRACT FROM AUTHOR]

In this paper, a novel unimodal chaotic system is presented which has stable Lyapunov exponents, a wider range of parameters and a larger phase space. In order to generate evenly distributed chaotic sequences, a general homogenization scheme is proposed with a rigorous mathematical proof. To generate high-quality pseudo-random number sequences, a PRNG scheme based on cross-coupling is designed. Theoretical derivation and experimental analysis fully demonstrate that the proposed PRNG has the ability to produce high-security random numbers with excellent random characteristics. [ABSTRACT FROM AUTHOR]

Piecewise-linear terrains ("roofs") over simple polygons were first studied by Aichholzer et al. (J. UCS 1995) in their work on straight skeletons of polygons. We show how to construct a roof over the polygonal footprint of a building that has minimum or maximum volume among all roofs that drain water. Our algorithm for computing such a roof extends the standard plane-sweep approach known from the theory of straight skeletons by additional events. For both types of roofs our algorithm runs in 𝒪 (n 3 log n) time for a simple polygon with n vertices. [ABSTRACT FROM AUTHOR]

We consider a quantum system consisting of two subsystems (open system and environment). We have proved that the Wigner function of an open system is the integral of the Wigner function of a larger system with respect to coordinates of the phase space of the classical subsystem corresponding to the entourage. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to formulate and prove an analogue of the classical Heisenberg–Pauli–Weyl uncertainty inequality for connected nilpotent Lie groups with noncompact center. Representation theory and a localized Plancherel formula play an important role in the proof. [ABSTRACT FROM AUTHOR]

In this paper, we explicitly work out the subfactor planar algebra P (N ⊂ Q) for an intermediate subfactor N ⊂ Q ⊂ M of an irreducible subfactor N ⊂ M of finite index. We do this in terms of the subfactor planar algebra P (N ⊂ M) by showing that if T is any planar tangle, the associated operator Z T (N ⊂ Q) can be read off from Z T (N ⊂ M) by a formula involving the so-called biprojection corresponding to the intermediate subfactor N ⊂ Q ⊂ M and a scalar α (T) carefully chosen so as to ensure that the formula defining Z T (N ⊂ Q) is multiplicative with respect to composition of tangles. Also, the planar algebra of Q ⊂ M can be obtained by applying these results to M ⊂ M 1 . We also apply our result to the example of a semi-direct product subgroup-subfactor. [ABSTRACT FROM AUTHOR]

We prove a result on the relationship between the relative conormal space of an analytic function f on affine space and the relative conormal space of f restricted to a hyperplane slice, at a point where the relative conormal space of f is "microlocally trivial". This result is intended to be used as a lemma to prove other conormal results by induction via hyperplane slicing. We present two proofs, one algebraic and one topological, since the methods may lead to other results in this area. [ABSTRACT FROM AUTHOR]

An injective k -coloring of a graph G is a mapping c: V (G) → { 1 , 2 , ... , k } such that c (u) ≠ c (v) whenever u , v have a common neighbor in G. A list assignment of a graph G is a mapping L that assigns a color list L (v) to each vertex v ∈ V (G). Given a list assignment L of G , an injective coloring φ of G is called an injective L -coloring if φ (v) ∈ L (v) for every v ∈ V (G). In this paper, we show that if G is a planar graph with girth g ≥ 5 , then χ i l (G) ≤ Δ (G) + 4 if Δ (G) ≥ 1 1. [ABSTRACT FROM AUTHOR]

Given an undirected graph G = (V , E) with a weight function c ∈ R E , and a positive integer K , the Kth Traveling Salesman Problem (Kth TSP) is to find K Hamilton cycles H 1 , H 2 , ... , H K such that, for any Hamilton cycle H ∉ { H 1 , H 2 , ... , H K } , we have c (H) ≥ c (H i) , i = 1 , 2 , ... , K. This problem is NP-hard even for K fixed. We prove that Kth TSP is pseudopolynomial when TSP is polynomial. [ABSTRACT FROM AUTHOR]

Generalized ring signcryption (GRSC) can realize ring signature and ring signcryption functions with only one key pair and one algorithm. It is very useful for a system with a large number of users, or whose function may be changed, or with limited storage space. We give a formal definition and security model of GRSC in the certificate-based cryptosystem setting and propose a concrete scheme by using bilinear pairings. The confidentiality of our scheme can be proved under the GBDH and CDH assumptions and the unforgeability of our scheme can be proved under G D H ′ and CDH assumptions in the random oracle model, and what is more, our scheme has unconditional anonymity. Compared with other certificateless ring signcryption schemes that use bilinear pairings, it is a highly efficient one. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to further explore the complexity of fuzzified dynamical systems. Especially, we study several kinds of specification properties of Zadeh’s extension. Among other things, we discuss the “stronger” sensitivity on product dynamical systems of g-fuzzification. There are two major ingredients. Firstly, it is proved that the specification (respectively almost specification) property of the original system and its Zadeh’s extension is equivalent, when the original system has the shadowing property. Moreover, we study the ℱ -sensitivity (respectively multi-sensitivity) of g-fuzzification and its induced product dynamical system. [ABSTRACT FROM AUTHOR]

In this paper, we prove Adams inequality with exact growth condition in the four-dimensional hyperbolic space ℍ 4 , ∫ ℍ 4 e 3 2 π 2 u 2 − 1 ( 1 + | u | ) 2 d v g ≤ C ∥ u ∥ L 2 ( ℍ 4 ) 2 , ( 0. 1 ) for all  u ∈ C c ∞ ( ℍ 4 )  with  ∫ ℍ 4 ( P 2 u ) u d v g ≤ 1. We will also establish an Adachi–Tanaka-type inequality in this setting. Another aspect of this paper is the Lions lemma in the hyperbolic space. We prove Lions lemma for the Moser functional and for a few cases of the Adams functional on the whole hyperbolic space. [ABSTRACT FROM AUTHOR]

By using the Lyapunov–Schmidt reduction method without perturbation, we consider existence results for the conformal scalar curvature on S n ( n ≥ 3 ) when the prescribed function (after being projected to I R n ) has two close critical points, which have the same value (positive), equal “flatness” (“twin”; flatness < n − 2 ), and exhibit maximal behavior in certain directions (“pseudo-peaks”). The proof relies on a balance between the two main contributions to the reduced functional — one from the critical points and the other from the interaction of the two bubbles. [ABSTRACT FROM AUTHOR]

Regular string-to-string functions enjoy a nice triple characterization through deterministic two-way transducers (2DFT), streaming string transducers (SST) and MSO definable functions. This result has recently been lifted to FO definable functions, with equivalent representations by means of aperiodic 2DFT and aperiodic 1-bounded SST, extending a well-known result on regular languages. In this paper, we give three direct transformations: i) from 1-bounded SST to 2DFT, i i) from 2DFT to copyless SST, and i i i) from k -bounded to 1 -bounded SST. We give the complexity of each construction and also prove that they preserve the aperiodicity of transducers. As corollaries, we obtain that FO definable string-to-string functions are equivalent to SST whose transition monoid is finite and aperiodic, and to aperiodic copyless SST. [ABSTRACT FROM AUTHOR]

We prove connections between one-variable word equations and three-variable constant-free word equations, and use them to prove that the number of equations in an independent system of three-variable constant-free equations is at most logarithmic with respect to the length of the shortest equation in the system. We also study two well-known conjectures. The first conjecture claims that there is a constant c such that every one-variable equation has either infinitely many solutions or at most c. The second conjecture claims that there is a constant c such that every independent system of three-variable constant-free equations with a nonperiodic solution is of size at most c. We prove that the first conjecture implies the second one, possibly for a different constant. [ABSTRACT FROM AUTHOR]

A nondeterministic finite automaton is unambiguous if it has at most one accepting computation on every input string. We investigate the state complexity of basic regular operations on languages represented by unambiguous finite automata. We get tight upper bounds for reversal (n), intersection (m n), left and right quotients ( 2 n − 1), positive closure ( 3 4 2 n − 1), star ( 3 4 2 n ), shuffle ( 2 m n − 1), and concatenation ( 3 4 2 m + n − 1). To prove tightness, we use a binary alphabet for intersection and left and right quotients, a ternary alphabet for star and positive closure, a five-letter alphabet for shuffle, and a seven-letter alphabet for concatenation. For complementation, we reduce the trivial upper bound 2 n to 2 0. 7 8 5 6 n + log n . We also get some partial results for union and square. [ABSTRACT FROM AUTHOR]

We contribute to the study of square-free words. The classical notion of a square-free word has a natural generalization to partial words, studied in several papers since 2008. We prove that the maximal density of wildcards in the ternary infinite square-free partial word is surprisingly big: 3 / 1 6. Further we show that the density of wildcards in a finitary infinite square-free partial words is at most 1 / 3 and this bound is reached by a quaternary word. We demonstrate that partial square-free words can be viewed as “usual” square-free words with some letters replaced by wildcards and introduce the corresponding characteristic of infinite square-free words, called flexibility. The flexibility is estimated for some important words and classes of words; an interesting phenomenon is the existence of “rigid” square-free words, having no room for wildcards at all. [ABSTRACT FROM AUTHOR]

The well-known synchronous context-free grammars (SCFGs) and synchronous tree-substitution grammars (STSGs), both of which are used as tree-to-tree translation models in statistical machine translation are investigated. Their composition hierarchies are established in both the unweighted as well as the weighted case. More precisely, it is shown that SCFGs are closed under composition in both cases and that there is a close connection between compositions of STSGs and compositions of certain tree transducers. With the help of the close ties, the composition closure of STSGs is identified in both cases as well. The results for the weighted case utilize a new lifting technique that might prove useful also in similar setups. [ABSTRACT FROM AUTHOR]

We prove the effective closure under complementation of the class of languages of scattered and countable N -free posets recognized by branching automata. [ABSTRACT FROM AUTHOR]

The first paper in this series introduced the notion of term to term operation continuity for finite groupoids, and proved that two testable conditions on a finite groupoid imply that it is term continuous (TC). The second presented an evolution inspired algorithm for finding terms for operations, and gave experimental evidence that, in general, it was successful exactly when the groupoid was both idemprimal and TC. In this paper, we describe a new class of algorithms for finding terms which brings these results together. Theorems about idemprimality and term continuity show how each of these two properties impact our algorithms. They lead to a final explanation for the success of our algorithms when the groupoid is both idemprimal and TC. [ABSTRACT FROM AUTHOR]

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients. [ABSTRACT FROM AUTHOR]

We prove that a weak -Fano -fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak -Fano -fold. We also treat a stacky proof of the unobstructedness of deformations of a -Fano -fold. [ABSTRACT FROM AUTHOR]

Parity games can be used to solve satisfiability, verification and controller synthesis problems. As part of an effort to better understand their nature, or the nature of the problems they solve, preorders on parity games have been studied. Defining these relations, and in particular proving their transitivity, has proven quite difficult on occasion. We propose a uniform way of lifting certain preorders on Kripke structures to parity games and study the resulting preorders. We explore their relation with parity game preorders from the literature and we study new relations. Finally, we investigate whether these preorders can also be obtained via modal characterisations. [ABSTRACT FROM AUTHOR]

The brain processes information about the environment via neural codes. The neural ideal was introduced recently as an algebraic object that can be used to better understand the combinatorial structure of neural codes. Every neural ideal has a particular generating set, called the canonical form, that directly encodes a minimal description of the receptive field structure intrinsic to the neural code. On the other hand, for a given monomial order, any polynomial ideal is also generated by its unique (reduced) Gröbner basis with respect to that monomial order. How are these two types of generating sets — canonical forms and Gröbner bases — related? Our main result states that if the canonical form of a neural ideal is a Gröbner basis, then it is the universal Gröbner basis (that is, the union of all reduced Gröbner bases). Furthermore, we prove that this situation — when the canonical form is a Gröbner basis — occurs precisely when the universal Gröbner basis contains only pseudo-monomials (certain generalizations of monomials). Our results motivate two questions: (1) When is the canonical form a Gröbner basis? (2) When the universal Gröbner basis of a neural ideal is not a canonical form, what can the non-pseudo-monomial elements in the basis tell us about the receptive fields of the code? We give partial answers to both questions. Along the way, we develop a representation of pseudo-monomials as hypercubes in a Boolean lattice. [ABSTRACT FROM AUTHOR]

Given a group G with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of G is finitely generated and virtually abelian of rank at most 2. In particular, this gives a new proof of the above theorem for systolic groups. The main tools used in the proof are the Product Decomposition Theorem and the Flat Torus Theorem. [ABSTRACT FROM AUTHOR]

We prove that abelian subgroups of the outer automorphism group of a free group are quasi-isometrically embedded. Our proof uses recent developments in the theory of train track maps by Feighn–Handel. As an application, we prove the rank conjecture for Out(Fn). [ABSTRACT FROM AUTHOR]

A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as reversal. We prove a series of results concerning birecurrent sets. It is already known that any birecurrent set is completely reducible (that is, such that the minimal representation of its characteristic series is completely reducible). The main result of this paper characterizes completely reducible sets as linear combinations of birecurrent sets [ABSTRACT FROM AUTHOR]

In this paper, we give necessary and sufficient conditions for a cylindrical continuous local martingale to be the stochastic integral with respect to a cylindrical Brownian motion. In particular, we consider the class of cylindrical martingales with closed operator-generated covariations. We also prove that for every cylindrical continuous local martingale M there exists a time change τ such that M∘τ is Brownian representable. [ABSTRACT FROM AUTHOR]

Let (Xt)t≥0 denote a non-commutative monotone Lévy process. Let ω=(ω(t))t≥0 denote the corresponding monotone Lévy noise, i.e. formally ω(t)=ddtXt. A continuous polynomial of ω is an element of the corresponding non-commutative L2-space L2(τ) that has the form ∑i=0n〈ω⊗i,f(i)〉, where f(i)∈C0(ℝ+i). We denote by CP the space of all continuous polynomials of ω. For f(n)∈C0(ℝ+n), the orthogonal polynomial 〈P(n)(ω),f(n)〉 is defined as the orthogonal projection of the monomial 〈ω⊗n,f(n)〉 onto the subspace of L2(τ) that is orthogonal to all continuous polynomials of ω of order ≤n−1. We denote by OCP the linear span of the orthogonal polynomials. Each orthogonal polynomial 〈P(n)(ω),f(n)〉 depends only on the restriction of the function f(n) to the set {(t1,…,tn)∈ℝ+n|t1≥t2≥⋯≥tn}. The orthogonal polynomials allow us to construct a unitary operator J:L2(τ)→𝔽, where 𝔽 is an extended monotone Fock space. Thus, we may think of the monotone noise ω as a distribution of linear operators acting in 𝔽. We say that the orthogonal polynomials belong to the Meixner class if CP=OCP. We prove that each system of orthogonal polynomials from the Meixner class is characterized by two parameters: λ∈ℝ and η≥0. In this case, the monotone Lévy noise has the representation ω(t)=∂t†+λ∂t†∂t+∂t+η∂t†∂t∂t. Here, ∂t† and ∂t are the (formal) creation and annihilation operators at t∈ℝ+ acting in 𝔽. [ABSTRACT FROM AUTHOR]

The extension of averaging procedure for operator-valued function is defined by means of the integration of measurable map with respect to complex-valued measure or pseudomeasure. The averaging procedure of one-parametric semigroups of linear operators based on Chernoff equivalence for operator-valued functions is constructed. The initial value problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of free motion. It is established that in these examples the solution of evolutionary equation can be obtained by applying the constructed averaging procedure to the random translation operators in classical coordinate space. [ABSTRACT FROM AUTHOR]

Given a quantum permutation group G⊂SN+, with orbits having the same size K, we construct a universal matrix model π:C(G)→MK(C(X)), having the property that the images of the standard coordinates uij∈C(G) are projections of rank ≤1. Our conjecture is that this model is inner faithful under suitable algebraic assumptions, and is in addition stationary under suitable analytic assumptions. We prove this conjecture for the classical groups, and for several key families of group duals. [ABSTRACT FROM AUTHOR]

In this paper, we prove a central limit theorem and establish a moderate deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by [6] plays an important role. [ABSTRACT FROM AUTHOR]

First, we prove an almost sure local central limit theorem for lattice random walks in the plane. The corresponding version for random walks in the line has been considered previously by the author. This gives us an extension of Pólya's Recurrence Theorem, namely we consider an appropriate subsequence of the random walk and give the asymptotic number of returns to the origin and other states. Secondly, we prove an almost sure local central limit theorem for (not necessarily lattice) random walks in the line or in the plane, which will also give us quantitative recurrence results. Finally, we prove a version of the almost sure central limit theorem for multidimensional random walks. This is done by exploiting a technique developed by the author. [ABSTRACT FROM AUTHOR]

Let and be the local Hardy space in the sense of D. Goldberg. In this paper, the authors establish two bilinear decompositions of the product spaces of and their dual spaces. More precisely, the authors prove that and, for any , , where denotes the local BMO space, , for any and , the inhomogeneous Lipschitz space and a variant of the local Orlicz-Hardy space related to the Orlicz function for any which was introduced by Bonami and Feuto. As an application, the authors establish a div-curl lemma at the endpoint case. [ABSTRACT FROM AUTHOR]